Advances in Dynamic Equations on Time Scales

The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam. Of a great deal of interest are methods being intro duced for dynamic equations on time scales, which now explain some discrepancies that have been encountered when results for differential equations and their dis crete counterparts have been independently considered. The explanations of these seeming discrepancies are incidentally producing unifying results via time scales methods. The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing. It has been created in order to unify continuous and discrete analysis, and it allows a simultaneous treatment of dif ferential and difference equations, extending those theories to so-called dynamic equations. An introduction to this subject is given in Dynamic Equations on Time Scales: An Introduction with Applications (MARTIN BOHNER and ALLAN PETER SON, Birkhauser, 2001 [86]). The current book is designed to supplement this introduction and to offer access to the vast literature that has already emerged in this field. It consists of ten chapters, written by an international team of 21 experts in their areas, thus providing an overview of the recent advances in the theory on time scales. We want to emphasize here that this book is not just a collection of papers by different authors.

The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis. This work goes beyond an earlier introductory text "Dynamic Equations on Time Scales: An Introduction with Applications" (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level. It will also be valuable to pure and applied mathematicians in the field.

1. Introduction to the Time Scales Calculus.- 2. Some Dynamic Equations.- 3. Nabla Dynamic Equations.- 4. Second Order Self-Adjoint Equations with Mixed Derivatives.- 5. Riemann and Lebesgue Integration.- 6. Lower and Upper Solutions of Boundary Value Problems.- 7. Positive Solutions of Boundary Value Problems.- 8. Disconjugacy and Higher Order Dynamic Equations.- 9. Boundary Value Problems on Infinite Intervals.- 10. Symplectic Dynamic Systems.